Title: Optimum designs for mixtures with relational constraints on the components

Authors: Manisha Pal; Nripes Kumar Mandal

Addresses: Department of Statistics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata 700019, India ' Department of Statistics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata 700019, India

Abstract: In many experimentations with mixtures, the classical mixture models are found to be inappropriate to describe the response. In pharmaceutical research, for example, the components of the mixture are often classified into groups and the proportions of different groups in the mixture are fixed. This results in relational constraints on the mixing components. In the paper, we study a mixture model appropriate in such a situation. We attempt to find optimum designs for estimation of parameters in the model, and also for estimation of the optimum proportions of components in a group. The support points of the optimum designs are found to belong to the union of barycentres of the domains of the groups involved.

Keywords: mixture experiments; relational constraints; major components; minor components; D-optimality; trace optimality; optimal design; mixtures; pharmaceutical research; mixture models; modelling.

DOI: 10.1504/IJEDPO.2013.055740

International Journal of Experimental Design and Process Optimisation, 2013 Vol.3 No.3, pp.276 - 293

Received: 09 Dec 2012
Accepted: 13 Jan 2013
Published online: 02 Jul 2014 *

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